Random color in materials to not change when I copy the objects
As Carlo's comment suggested, you could bake the color onto a texture.


Activate the Texture Atlas Addon.
Add an empty image texture.
Select all objects and unwrap them using the texture atlas addon.See the texture atlas documentation for more instructions on this addons usage.
Bake the Diffuse Color only using very few render samples!
Replace the Object Info random output with the image textures output.